Multiply the following complex numbers: $({-3-2i}) \cdot ({4+2i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3-2i}) \cdot ({4+2i}) = $ $ ({-3} \cdot {4}) + ({-3} \cdot {2}i) + ({-2}i \cdot {4}) + ({-2}i \cdot {2}i) $ Then simplify the terms: $ (-12) + (-6i) + (-8i) + (-4 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -12 + (-6 - 8)i - 4i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -12 + (-6 - 8)i - (-4) $ The result is simplified: $ (-12 + 4) + (-14i) = -8-14i $